Place sliced steak into a gallon sized ziplock baggie. Set aside.
In a medium sized bowl, whisk together oil, vinegar, garlic, salt, and pepper.
Pour half over steak and allow to marinate in the fridge for 30 minutes - 8 hours (I shoot for at least a few hours).
Place onion, pepper, and mushrooms in a large bowl and toss with the reserved marinade. Set aside and allow to marinate for up to 30 minutes.
Heat a large sauté pan over medium-high/high heat.
Carefully place the contents of the ziplock baggie (meat + marinade) in the hot pan and cook for 3-5 minutes, or until the steak is cooked to your liking.
Remove and drain liquid (reserve for dipping, if desired). Set aside.
In the same hot pan, cook veggies until tender, about 3-5 minutes.
Turn off the heat, then stir the meat back into the pan. Taste and re-season, if necessary.
Top meat and veggie mixture with cheese slices.
Cover, and allow the cheese to melt, about 3-5 minutes.